Abstract
f (R) supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains Rn with n greater than two. We remove the ghost in f (R) supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism [1]. We show that the mechanism removes the ghost super-multiplet but also terms including Rn with n ≥ 3, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Fujimori, M. Nitta and Y. Yamada, Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?, JHEP 09 (2016) 106 [arXiv:1608.01843] [INSPIRE].
M. Ostrogradski, Mémoires sur les équations différentielles, relatives au problème des isopérimètres (in French), Mem. Ac. St. Petersbourg 6 (1850) 385 [INSPIRE].
R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
T. Kobayashi, M. Yamaguchi and J. Yokoyama, Generalized G-inflation: inflation with the most general second-order field equations, Prog. Theor. Phys. 126 (2011) 511 [arXiv:1105.5723] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
F. Farakos, C. Germani and A. Kehagias, On ghost-free supersymmetric galileons, JHEP 11 (2013) 045 [arXiv:1306.2961] [INSPIRE].
D. Roest, P. Werkman and Y. Yamada, Internal supersymmetry and small-field goldstini, arXiv:1710.02480 [INSPIRE].
A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
H.A. Buchdahl, Non-linear Lagrangians and cosmological theory, Mon. Not. Roy. Astron. Soc. 150 (1970) 1 [INSPIRE].
A. De Felice and S. Tsujikawa, f (R) theories, Living Rev. Rel. 13 (2010) 3 [arXiv:1002.4928] [INSPIRE].
S. Nojiri, S.D. Odintsov and V.K. Oikonomou, Modified gravity theories on a nutshell: inflation, bounce and late-time evolution, Phys. Rept. 692 (2017) 1 [arXiv:1705.11098] [INSPIRE].
S.J. Gates Jr., Why auxiliary fields matter: the strange case of the 4D, N = 1 supersymmetric QCD effective action, Phys. Lett. B 365 (1996) 132 [hep-th/9508153] [INSPIRE].
S.J. Gates Jr., Why auxiliary fields matter: the strange case of the 4D, N = 1 supersymmetric QCD effective action. 2, Nucl. Phys. B 485 (1997) 145 [hep-th/9606109] [INSPIRE].
I. Antoniadis, E. Dudas and D.M. Ghilencea, Supersymmetric models with higher dimensional operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].
E. Dudas and D.M. Ghilencea, Effective operators in SUSY, superfield constraints and searches for a UV completion, JHEP 06 (2015) 124 [arXiv:1503.08319] [INSPIRE].
J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P(X, \( \phi \)) and the ghost condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].
J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
M. Koehn, J.-L. Lehners and B.A. Ovrut, Higher-derivative chiral superfield actions coupled to N = 1 supergravity, Phys. Rev. D 86 (2012) 085019 [arXiv:1207.3798] [INSPIRE].
M. Koehn, J.-L. Lehners and B. Ovrut, Ghost condensate in N = 1 supergravity, Phys. Rev. D 87 (2013) 065022 [arXiv:1212.2185] [INSPIRE].
T. Fujimori, M. Nitta, K. Ohashi, Y. Yamada and R. Yokokura, Ghost-free vector superfield actions in supersymmetric higher-derivative theories, JHEP 09 (2017) 143 [arXiv:1708.05129] [INSPIRE].
I.L. Buchbinder, S. Kuzenko and Z. Yarevskaya, Supersymmetric effective potential: superfield approach, Nucl. Phys. B 411 (1994) 665 [INSPIRE].
I.L. Buchbinder, S.M. Kuzenko and A. Yu. Petrov, Superfield chiral effective potential, Phys. Lett. B 321 (1994) 372 [INSPIRE].
A.T. Banin, I.L. Buchbinder and N.G. Pletnev, On quantum properties of the four-dimensional generic chiral superfield model, Phys. Rev. D 74 (2006) 045010 [hep-th/0606242] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, The one-loop effective potential of the Wess-Zumino model revisited, JHEP 09 (2014) 135 [arXiv:1407.5270] [INSPIRE].
M. Nitta and S. Sasaki, Higher derivative corrections to manifestly supersymmetric nonlinear realizations, Phys. Rev. D 90 (2014) 105002 [arXiv:1408.4210] [INSPIRE].
F. Farakos and A. Kehagias, Emerging potentials in higher-derivative gauged chiral models coupled to N = 1 supergravity, JHEP 11 (2012) 077 [arXiv:1207.4767] [INSPIRE].
S. Sasaki, M. Yamaguchi and D. Yokoyama, Supersymmetric DBI inflation, Phys. Lett. B 718 (2012) 1 [arXiv:1205.1353] [INSPIRE].
S. Aoki and Y. Yamada, Inflation in supergravity without Kähler potential, Phys. Rev. D 90 (2014) 127701 [arXiv:1409.4183] [INSPIRE].
S. Aoki and Y. Yamada, Impacts of supersymmetric higher derivative terms on inflation models in supergravity, JCAP 07 (2015) 020 [arXiv:1504.07023] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Extended supersymmetry and BPS solutions in baby Skyrme models, JHEP 05 (2013) 108 [arXiv:1304.0774] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
M. Nitta and S. Sasaki, BPS states in supersymmetric chiral models with higher derivative terms, Phys. Rev. D 90 (2014) 105001 [arXiv:1406.7647] [INSPIRE].
M. Nitta and S. Sasaki, Classifying BPS states in supersymmetric gauge theories coupled to higher derivative chiral models, Phys. Rev. D 91 (2015) 125025 [arXiv:1504.08123] [INSPIRE].
S. Bolognesi and W. Zakrzewski, Baby Skyrme model, near-BPS approximations and supersymmetric extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [INSPIRE].
J.M. Queiruga, Baby Skyrme model and fermionic zero modes, Phys. Rev. D 94 (2016) 065022 [arXiv:1606.02869] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, A supersymmetric Skyrme model, JHEP 02 (2016) 074 [arXiv:1512.07557] [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, Topological solitons in the supersymmetric Skyrme model, JHEP 01 (2017) 014 [arXiv:1608.03526] [INSPIRE].
J.M. Queiruga, Skyrme-like models and supersymmetry in 3 + 1 dimensions, Phys. Rev. D 92 (2015) 105012 [arXiv:1508.06692] [INSPIRE].
J.M. Queiruga and A. Wereszczynski, Non-uniqueness of the supersymmetric extension of the O(3) σ-model, JHEP 11 (2017) 141 [arXiv:1703.07343] [INSPIRE].
M. Eto, T. Fujimori, M. Nitta, K. Ohashi and N. Sakai, Higher derivative corrections to non-Abelian vortex effective theory, Prog. Theor. Phys. 128 (2012) 67 [arXiv:1204.0773] [INSPIRE].
M. Nitta, S. Sasaki and R. Yokokura, Spatially modulated vacua in relativistic field theories, arXiv:1706.02938 [INSPIRE].
M. Nitta, S. Sasaki and R. Yokokura, Supersymmetry breaking in spatially modulated vacua, Phys. Rev. D 96 (2017) 105022 [arXiv:1706.05232] [INSPIRE].
S. Cecotti and S. Ferrara, Supersymmetric Born-Infeld lagrangians, Phys. Lett. B 187 (1987) 335 [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, Nonlinear selfduality and supergravity, JHEP 02 (2003) 038 [hep-th/0212039] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, On the component structure of N = 1 supersymmetric nonlinear electrodynamics, JHEP 05 (2005) 012 [hep-th/0501172] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, Matter coupled Dirac-Born-Infeld action in four-dimensional N = 1 conformal supergravity, Phys. Rev. D 92 (2015) 025017 [arXiv:1504.01221] [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Structure of the scalar potential in general N = 1 higher derivative supergravity in four-dimensions, Phys. Lett. B 187 (1987) 321 [INSPIRE].
F. Farakos, S. Ferrara, A. Kehagias and M. Porrati, Supersymmetry breaking by higher dimension operators, Nucl. Phys. B 879 (2014) 348 [arXiv:1309.1476] [INSPIRE].
S.M. Kuzenko and S. Theisen, Supersymmetric duality rotations, JHEP 03 (2000) 034 [hep-th/0001068] [INSPIRE].
S.M. Kuzenko and S. Theisen, Nonlinear selfduality and supersymmetry, Fortsch. Phys. 49 (2001) 273 [hep-th/0007231] [INSPIRE].
S.M. Kuzenko, The Fayet-Iliopoulos term and nonlinear self-duality, Phys. Rev. D 81 (2010) 085036 [arXiv:0911.5190] [INSPIRE].
S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1, Phys. Lett. B 190 (1987) 86 [INSPIRE].
S. Ferrara, A. Kehagias and A. Riotto, The imaginary Starobinsky model and higher curvature corrections, Fortsch. Phys. 63 (2015) 2 [arXiv:1405.2353] [INSPIRE].
F. Farakos, S. Ferrara, A. Kehagias and D. Lüst, Non-linear realizations and higher curvature supergravity, Fortsch. Phys. 65 (2017) 1700073 [arXiv:1707.06991] [INSPIRE].
G.A. Diamandis, B.C. Georgalas, K. Kaskavelis, A.B. Lahanas and G. Pavlopoulos, Deforming the Starobinsky model in ghost-free higher derivative supergravities, Phys. Rev. D 96 (2017) 044033 [arXiv:1704.07617] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K., (2012) [INSPIRE].
R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP 06 (2013) 028 [arXiv:1306.3214] [INSPIRE].
F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky model of inflation from supergravity, Nucl. Phys. B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].
S.V. Ketov and T. Terada, Old-minimal supergravity models of inflation, JHEP 12 (2013) 040 [arXiv:1309.7494] [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev. D 17 (1978) 3179 [INSPIRE].
M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. B 76 (1978) 54 [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Simplifications of conformal supergravity, Phys. Rev. D 19 (1979) 3166 [INSPIRE].
T. Kugo and S. Uehara, Conformal and Poincaré tensor calculi in N = 1 supergravity, Nucl. Phys. B 226 (1983) 49 [INSPIRE].
M. Ozkan and Y. Pang, R n extension of Starobinsky model in old minimal supergravity, Class. Quant. Grav. 31 (2014) 205004 [arXiv:1402.5427] [INSPIRE].
S. Ferrara, L. Girardello, T. Kugo and A. Van Proeyen, Relation between different auxiliary field formulations of N = 1 supergravity coupled to matter, Nucl. Phys. B 223 (1983) 191 [INSPIRE].
S. Cecotti and R. Kallosh, Cosmological attractor models and higher curvature supergravity, JHEP 05 (2014) 114 [arXiv:1403.2932] [INSPIRE].
R. Kallosh, A. Linde and D. Roest, Superconformal inflationary α-attractors, JHEP 11 (2013) 198 [arXiv:1311.0472] [INSPIRE].
J.J.M. Carrasco, R. Kallosh, A. Linde and D. Roest, Hyperbolic geometry of cosmological attractors, Phys. Rev. D 92 (2015) 041301 [arXiv:1504.05557] [INSPIRE].
M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1712.05017
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Fujimori, T., Nitta, M., Ohashi, K. et al. Ghostbusters in f (R) supergravity. J. High Energ. Phys. 2018, 102 (2018). https://doi.org/10.1007/JHEP05(2018)102
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2018)102